Deep learning and superoscillatory speckles empowered multimode fiber probe for in situ nano-displacement detection and micro-imaging.

High-precision metrology has laid the foundation for semiconductor fabrication and life sciences. However, existing displacement measurement approaches are incapable of performing flexible probing within complex equipment interiors. Here, we present a in situ, non-contact nano-displacement measurement approach. Leveraging a multimode fiber probe empowered by deep learning, fine feature information can be efficiently extracted from superoscillatory speckles, achieving single-ended detection with 10 nm resolution and 99.95% accuracy. A physical model is established to correlate the displacement with higher-order modes proportion in the fiber. Sub-millimeter-sized probe enables detecting targets with different structures in confined spaces. Robust recognition is achieved through joint learning, under varying fiber bending conditions and different metal materials. With extreme compression ratios of less than 0.1%, the system delivers high accuracy, low training costs, and high-speed processing. The imaging capability of the probe is also experimentally validated, proving potential as a powerful tool in applications such as lithography, weak force sensing, and super-resolution micro-endoscopy.